We consider the problem of finding a global minimizer (or maximizer) of an unknown (black-box) objective function \(f\) :
\(\mathbf {s^*} \in _{\mathbf {s} \in }f(\mathbf {s}),\) 
where \(\)  is some input design space of interest in \(D\)  dimensions.
The problem addressed in this paper is the optimization of a
(possibly noisy) function \(f:\rightarrow \)  with lower and upper bounds on the problem variables.
The variables defining \(\)  can be real (continuous), integer, ordinal, and categorical as in [1]}. We assume that the function \(f\)  is in general expensive to evaluate
and that the derivatives of \(f\)  are in general not available.
The function \(f\)  is called black box because we cannot access other information than the output \(y\)  given an input value \(\mathbf {s}\) .
